Markov Chains

Valérie Girardin and Nikolaos Limnios
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Valérie Girardin: Université de Caen Normandie, Laboratoire de Mathématiques Nicolas Oresme
Nikolaos Limnios: Université de Technologie de Compiègne, Laboratoire de Mathématiques Appliquées de Compiègne

Chapter 3 in Applied Probability, 2018, pp 113-173 from Springer

Abstract: Abstract This chapter investigates the homogeneous discrete-time Markov chains with countable—finite or denumerable—state spaces, also called discrete. Markov chains generalize sequences of independent random variables to variables linked by a simple dependence relation. They model for example, phase transitions of substances between solid, liquid and gaseous states, passages of systems between up and down states, etc. A random sequence ( X n ) n ∈ ℕ $$(X_n)_{n\in \scriptstyle \mathbb {N}}$$ is a Markov chain if its future values depend on its previous values only through its present value, the so-called Markov property. The index n is interpreted as a time, even when it is the n-th trial or step in a process.

Date: 2018
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DOI: 10.1007/978-3-319-97412-5_3

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